What is the integral of 4x(sec^2(x)-tan^2(x)) ?

The integral of 4x(sec^2(x)-tan^2(x)) is 2x^2+C

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integral of 4x(sec^2(x)-tan^2(x))

\int 4 x (sec^{2} (x) - tan^{2} (x)) d x

2 x^{2} + C

Solution steps

\int 4 x (sec^{2} (x) - tan^{2} (x)) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 4 \cdot \int x (sec^{2} (x) - tan^{2} (x)) d x

Simplify

x (sec^{2} (x) - tan^{2} (x)) : x

= 4 \cdot \int x d x

Apply the Power Rule

: \frac{x ^{2}}{2}

= 4 \cdot \frac{x ^{2}}{2}

Simplify

4 \cdot \frac{x ^{2}}{2} : 2 x^{2}

= 2 x^{2}

Add a constant to the solution

= 2 x^{2} + C

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What is the integral of 4x(sec^2(x)-tan^2(x)) ?
The integral of 4x(sec^2(x)-tan^2(x)) is 2x^2+C